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PreCalc 11

Portfolio Final-

Amelia Baca

PreCalc 11

Cover Letter

 

Cover Letter

 

 

Pythagorean Theorem and Coordinate Geometry-

 

In this unit, we learned many things; the relationships between coordinates in angels, lines, shapes, and different areas of change. This was the basis of our learning. To apply this, the equation is a^2 + b^2=c^2. Each a and b are the sides of the RIGHT triangle. And c equals the hypotenuse. We applied this mathematical function to many different aspects of this unit. In this unit, we had to locate the midpoint and distance of shapes and points. We then learned that,  distance =√((x_2-x_1)²+(y_2-y_1)²). Then, midpoint=add both of the x coordinates then divide the sum by 2. Lastly, add both y coordinates then divide by 2. We used both of these in work “Proving the Distance 2” and “POW Fire! Fire!” (located below). 

 

Circles and the Square-Cube Law-

 

The circles and square-cube law is the relationship between surface area and volume in the change of size. To understand this concept you first have to identify, area refers to 2d planes when volume refers to 3d. In this unit, we used this concept in both “POW Fire! Fire!” and “Proving the Distance” (located below). The point of this mathematics is to allow you to find the difference between area and volume and how in different circumstances, they work together. For example, when a shape increases in the size, the surface area does not increase at the rate the volume does. 

 

Proof-


Throughout this unit,  I applied these 2 functions in every piece of work I did. Even in work, where I did not think they would apply. I was able not only to identify these processes but also apply them to work which then lead to a bigger project. The two biggest pieces of work I applied these to were “POW Fire! Fire!’ and “Proving the Distance 1 & 2”. (Shown Below). Throughout this unit these two aspects connected to each and every assignment we did, these were the building blocks to this unit. In the work below you can see each aspect being used in my daily work. Then later applied to my end result.

Amelia Baca

PreCalc 11

Solution


 

Introduction, Process, and Solution

 

Introduction-

 

In this unit, there were two individuals; Maddie and Clyde. Their goal was to create an orchard on a large plot of land. They wanted to make a tree hideout. They want the outside to be surrounded by trees and an empty middle. But how? They have one requirement. Maddie and Clyde do not want you to be able to see in or out of the center of the orchard. In this problem, all we are given is the knowledge of 50  radius. We now need to help them figure out the length of time for this to be created, the area of the hideout, and the last line of sight from the orchard. 


 

Process and Justification-

 

To begin this process, you will need to apply all the former information given. Then try and represent the given data. (I drew a picture). The orchard radius is 50 which makes each unit 10 feet. This means the last line of sight will pass coordinate (25,½) and pass-through (50,1). Each tree begins at 2.5 inches and then over time will increase 1.5 inches per year. Next, we apply the math. 

 



 

Now, we want to find the last line of sight. After seeing this diagram, we know that we have a 90-degree angle. We now know the units for one triangle, which means we can apply this to the rest. This will help us find a solution. We will now look at triangle b (radius 6). We know this because the hypotenuse of triangle A is tangential to the circle. Next step, we need to find the hypotenuse of A so we can identify the units for triangle B. We next use the Pythagorean Theorem, after the math, the hypotenuse is the square root of 2501 or 50.0099990002. Next, we have to solve for radius.

 

 

 

We now know that the radius is 0.019996 units. Applying the 10 feet knowledge,  the radius is 2.4 in^2. Next using the area equation, A= 18.0883 in^2. Next, we apply that to find the radius, which is 2 x pi x r. So, 2.5 = 2 x pi x r. This gives us a radius of 0.398 inches. Then applying that to the area, you get A=0.497 in^2. And lastly, you subtract tree growth then divide the time time of growth (17.591 in^2 and 17.591 in^2 divided by 1.5 in^2). Finally, you receive a grand total of 11.73 years. This is the amount of time for the Orchard Hideout to be created. 


 

Solution-

 

After a vast amount of work, you are given a conclusion to how long. Using all aspects mentioned you come to a conclusion. For the Orchard Hideout to created from seed to complete, will take a total of 11.73  years, 8 months, 22 days, 4 hours, 46 minutes, and 36 seconds. 

Amelia Baca

PreCalc 11

Reflection

 

Reflection

Self-Reflection-

What is a key insight you have gained about yourself as a student in this unit?

 

In this unit, I have found myself doing a lot of self-exploration and reflecting. Coming into this year, I was extremely nervous and discouraged from being able to learn this math. I do not stove in my math classes compared to an English or social studies class. Personally, last year in math, I did not have the best experience. I struggled with the class itself, the content, and my confidence to do the math. The biggest thing I have learned from this unit is to ask for help. I struggle with speaking up at times which makes me more confused in the long run of things. This year one of my personal goals was to speak up and ask more questions. I strived best in in-person learning because I got hands-on help from my teacher and my fellow classmates. Being able to ask questions was highly beneficial to better understanding this tough curriculum we are now learning.


 

Content Reflection-

What did you think of the unit content?  Does it feel applicable to your life?  Did you feel challenged/bored? 

 

Personally, I enjoyed this unit in the end. When first given this unit, I would have no way been able to solve it. And in the end, I feel confident in all aspects of this unit (though some may be not as good as others). I felt extremely challenged to the point I started slacking off. I let the work get ahead of me and I fell behind leaving me to do a large amount of work in only a few days. I liked the content of this unit but at times I felt like it was being repetitive and non-needed. I have found that going from algebra to precalc was a large jump for me. In this unit, I struggled, I strived, I failed, and I achieved. I was able to learn from my mistakes and move on with added help. But this unit helped me lay down the base for calculus. Though I did struggle, in the end, I found success. 

 

Overview-

In conclusion, I enjoyed this unit though at times I did not find success. I gained new knowledge of math. And this unit helped me identify my strengths and weaknesses. I learned a large number of formulas, operations, etc. Though this was a large jump from algebra to Precalc, I was able to enjoy this unit and challenge myself. 

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